A "change of basis" is an action performed in linear algebra, whereby a change in fundamental structure yields an entirely new viewpoint. This blog began as a record of a pedagogical change of basis for me, and continues as an ongoing account of my thoughts as I design and direct courses in mathematics at the University of North Carolina, Asheville.

Sunday, April 22, 2007

As the semester draws to a close, I'm reflecting back on how well my classes went this term.

Useless, I know: I'm so self-conscious now about asking loaded and essentially pointless questions like "how did I do?", knowing as I do that the best measure of the success of a class is not whether the professor's plans were executed smoothly, not whether her or his lectures were flawless, but rather how much the students were able to learn from the class.

I know this, I know this, I know this. I know that to ask how I "did" as a teacher without knowing precisely how much my students have learned from the class assumes that effective learning is a result of effective professorial procedure, so assessment of that procedure yields an accurate measure of quality of learning.

Yet, as a product of the product-oriented academic establishment that continues to pile everything up into one heap to stamp it with a single letter grade (even while talking from the side of its mouth about portfolios, peer assessment, and learner-centered methodologies), I can't help asking: how well has it "gone"?

I'll soon find out from my end-of-term-evaluations how my students feel, but for the time being I include below some self-evaluation.

Calc I. Overall grade: A-

I feel this class has "gone" quite well. There's some room for improvement, but all in all I can't complain.

I've not taught Calc I for a year and a half now, and after having led four sections of Calc II, one of Calc III, and one of Advanced Calc, all since last teaching Calc I, I wasn't very fresh. I found myself stretching to come up with new ideas for mini-projects (that part went okay, I think), and awkwardly incorporating the team quizzes born in last semester's Linear Algebra class.

What's "gone" well? Class meetings in general have been smooth ones, and I feel that my presentation of the underlying concepts (for what they're worth) has been strong. The smooth flow of class truly has been the work of the students, who've shown nearly no inhibitions when it comes to working together, both in and outside of class. I feel I've developed a good rapport with most of the students, a sort of trust that makes our interactions more fruitful.

What's "gone" not so well? I feel that perhaps I've lingered too long on some topics. I'm not sure I've made as strong an effort as I should have to engage the students outside of the classroom, or to encourage them to do the homework. The "random grading" that I've done for the last four sections of Calc II hasn't gone over so well with the Calc I class, if one is to take any message from the relative infrequency of homework completion. I may rethink this form of assessment before Fall comes. But what will work best to get the students to do the work? Homework quizzes? Grading all of the homework?

Of course, as I've said at length above, it doesn't matter how well I "taught"; ultimately, the question that must be asked is "how well did they learn?" Only the students can answer this question. (Students: thoughts?)

Foundations. Overall grade: B

I started out the semester with exceedingly high hopes, and I'm not altogether certain I've met the goals I'd set out for myself (thus the relatively lackluster grade). I think what's hurt me most is my underestimation of the difficulty of the concepts we've covered: I've forgotten just how difficult it is to master the idea of induction, or how it's far from clear at first what is the structure of a proof by contraposition. I've forgotten that the idea of "relation" isn't immediately intuited, but rather takes time to understand. I've forgotten what it's like to be a budding mathematician, that in the beginning more than at any other time the art takes a great deal of patience and hard work to master, that that mastery comes more easily to some than to others, and that most students will struggle with it. As a consequence, I think I might have assumed that my students are at a higher stage of development as learners than they truly are, opening a chasm between me and my expectations on one side, and them and their abilities on the other. Might this be what's led to the recently-ballyhooed decline in attendance towards the semester's end? (It's hard to stay engaged if your efforts end only in frustration.)

Granted, it was my first time teaching this course at UNCA (and my second time teaching such a course anywhere), so I suppose I'm allowed to err in my assessment of their level of development as learners. I'll know this more well going into the same course next Fall.

Nevertheless, I can think of several students who have excelled as independent learners, who, I feel, have gained immeasurably from the class. I hope they recognize themselves.

To repeat a useless question, for what it's worth: what's "gone" well? The general dynamic of class, with its highly participatory nature, has been a healthy one, by and large. I've had compliments on this dynamic from a number of students who have found it effective, who have said that it makes them feel less anxious about the difficulties in approaching the math, having others to share those difficulties with. Overall, this class, which I've managed in more or less the same way I led Linear Algebra last semester, went far more smoothly than the latter class. (I have a feeling the few students...four, I think...that I've carried over from that class to this one would agree with me.) Students were more engaged in this current class, more eager to contribute, and less trepidatious, and I myself felt more at ease. I felt comfortable with the amount of "lecturing" that I did. I felt this balanced well with the student-centered portions of the class.

What's "gone" not so well? I'm not sure I did as well as I might have in managing the student homework presentations, particularly as regards students' peer evaluation of these presentations. For instance, I didn't challenge the students to challenge each other's solutions, I didn't force them to take the responsibility for the mathematics presented. I think I spent too much time worrying about how long the presentations were taking, and not enough time worrying about how well the students were guiding themselves and each other towards stronger, clearer proofs.

I'm also not sure that I did as well as I should have in demanding boilerplate proofs of everyone. But should I have asked for this?

It's like this: if I've got a student whose grasp of the most basic logical conventions, even at this end of the semester, is, to put it nicely, minimal (and there are a few such students in the class), the last thing I'm going to be worried about in their proofs is whether they ended their sentences with periods. Although good grammar leads automatically to stronger proofs, if the student's handling of the concept "if/then" is nothing more an awkward pawing, no amount of textual emendation short of out-and-out rewriting is going to make a clear proof out of a mish-mash of barely coherent semi-mathematical ramblings.

I'm not sure I'm making any sense.

Again, students: what do you feel?

Number Theory. Overall grade: A

Easy A. With knobs on. I've loved this class, I can't point to a single thing that I feel has gone poorly. The smallness of the class (not to mention the inherent motivation of the students) has led to nearly seamless in-class activities. The students' homework presentations have been strong ones, almost without exception. The worksheets I've constructed based on the text (the first text I've used in years that I feel strongly positively about) did a good job of distilling the essential information into class-long activity guides. The students have cooperated well with each other, have shown genuine interest in the subject, and have unswervingly followed my lead into some pretty dense and detailed detours (like the theory of arithmetic functions and basic analytic number theory). I've already heard from several of the students that they agree with this assessment: they've learned a lot, and they've had fun. This has been one of my favorite classes yet at UNCA.

There you have it. I hope my students will read and feel free to post their own comments (even if anonymously).

Wednesday, April 18, 2007

As promised, here's a shot of the fractal the kids and I put together this past Saturday:

Incidentally, while visiting James Madison U. this past Monday I mentioned the Multimedia Menger Sponge Project idea to my colleague Mandi (shout out, Mandi!), whose elementary ed students were busily building Level 2 cubes out of origami paper during my visit. She seemed pretty excited about the idea, as did several of my students whom I polled yesterday.

Saturday, April 14, 2007

Look, I understand that "things" come up unexpectedly: illnesses (ohhhhh...do I understand that one well), family emergencies, lottery winnings, superstardom, unexpected tickets to the Superbowl, including all-access passes to get onto the field while Prince is performing...These "things" come up, and they can come as a thief in the night.

Yet these "things" aren't the only things keeping you from coming to class. Other things, less sudden, yet more stealthy, things that don't pounce on you like a jungle cat leaping from the shadows but might rather overcome you slowly, wearing away at you as the semester gets on: excessive love of sleep, excessive love of pot, passive apathy, active antipathy, a malingering defeatist "I'm doing so poorly in this class how can hurt me more if I stop coming" attitude, fin-de-siècle ennui...any one of these things might stalk you quietly and drag you slowly down.

Please don't let these things overtake you, all right?

See, here's the thing: I like it when you come to class. I do. I like seeing you there, I like interacting with you. At the end of the day, I love what I do for a living. While in a particularly peeved mood yesternoon (brought about by, I might add, certain students exhibiting this Ninth Annoying Habit) I was musing to one of my best friends: "why didn't I take a job in industry? I'd be working nine-to-five, making twice what I make now, and I'd have none of the stress, none of the busyness." Of course, the answer came from my own lips not five seconds later: "because I'd hate that. It'd suck, and I'd hate it."

I love my job, every bit of it. I love math, I love math research, and math conferences and math committees...and above all I love teaching math. I love all of these things. I just get annoyed when you don't think it worth your time to come and share my joy. (Oh, and, by the way, your fellow students notice when you're not there, too: when only 15 people of the 23 who are registered for the course show up, your absence is distinctly palpable.)

Again, I'm not talking to those of you for whom "things" have come up. "Things" have been coming up regularly since the dawn of time, and as far as I can tell, "things" will keep coming up regularly for the rest of the foreseeable future. There's no getting around "things," but a quick phone call or e-mail to let me know about them when they do pop up might be nice.

I'm talking to those of you who've decided that it's just too much effort to come to class. Let me end this rant with this note for you.

When you miss class for an inexcusable reason, you send the following message, boldly and clearly, both to me and to your fellow students who do come regularly: "I have very little consideration for the enormous amount of time you spend in crafting learning experiences for me to take part in."

Hey, man, if that's the score, please do me a favor and don't register for the class in the first place.

Whew.

END OF RANT

So here's the deal with the Menger sponge.

While lying awake a couple of nights ago (I slept well last night, for the first time this week, thank you very much for asking!), my mind addled by codeine-laced cough syrup, I thought deeply of this fractally-formed creature. How came I to these ruminations?

Well, it began a couple of weeks ago, when we spent some time during the March 31st installment of our Super Saturday program working with fractals in the plane. At that time I had a chance to wow the kiddoes with a picture of a Menger sponge, namely this one, a shot of software engineer Jeannine Mosely, standing in front of the sponge she spent nine years building from business cards, with the help of hundreds of folks from around the country. Incidentally, there are 8000 cubes in this one, a "level-3" sponge. (By the way, The hijinx and hilarity continued this week. Just hours ago we wrapped up the today's class, spent assembling a Sierpinski pyramid out of several dozen folded pieces of recycled printer paper, affixed to one another with Scotch tape. [No pictures yet, my camera was at home. Next week! I promise.] The result is quite impressive, and the kids were proud of their achievement. Each took her or his turn holding the behemoth overhead, as though all had played an equal part in its construction. [Truly Jasmine, the lone female in the class whose time, already actively used to its full potential, was freed by not having anyone of her own sex to waste time with, contributed most of the student work on the project. I provided a goodly number of the little pyramids, while Umberto worked slowly yet diligently on his pile of triangles. The few pyramids he made he passed off to Jasmine so that she could skilfully fasten them together. Whether he was motivated by a simple crush or by a sense of pragmatism, recognizing her as the master builder, I'm not sure. In any case, it was cute.] The guts of the Menger sponge that never would be, 200 sheets of recycled printer paper with stenciled cube skeleta photocopied onto them, were left almost untouched. Too bad.) Now, I mean no insult to business cards and recycled printer paper (what better way is there for a piece of printer paper to end its practical life than to be made into a beautiful work of mathematical art?), but it must be admitted that these media are not so sexy as other materials one might choose to build fractals from. Plastic? Wood? Metal? Glass? Ceramic? Silk? The possibilities are endless.

What if, in the spirit of community projects such as Postsecret, people were asked to submit to a central source their own tiny cubes, 2 or 3 centimeters per side, made of whatever material they wished to use and decorated in any fashion desired, and these cubes were assembled lovingly by project coordinators who took care to build the structure by attaching cubes to one another in the manner specified by the contributors: "please ensure that the side bearing my name is not visible..."? Imagine a sponge stretching over 7 feet in any direction, made up of 160,000 (with all due respect, take that, Dr. Mosely!) 3x3x3 cubes of all manner of media, each cube telling a story of an individual contributor, as those submitting cubes could include stories, insights, comments on what the project means to them: "I chose to participate because..."

I'd be curious to see what people would have to say, about the project, about math in general. It's not so often that I get a chance to interact mathematically with people who know so much less about math than I do, with people whose love of math (if it's there at all) is not inherent: how do such people feel about things mathematical?

I don't know.

What do you think of this? Is it a codeine-made pipedream, or a worthwhile artistic undertaking? I'm truly tempted to try this out, but I'm not sure I'd want to start without some backing. Who's got my back? If you're out there reading this, let me know what you think, and ask your friends to check in and let me know what they think, too. Consider it an ad hoc committee on the creation of the Multimedia Menger Sponge Project. Let's get together, people!

Friday, April 13, 2007

As the semester really starts to heat up (don't you love the fast pace of these last few weeks?), I up and decide to come down with the mother of all colds.

To my students: I apologize for the raspiness (and sometimes absence) of my voice, and for any perceived shortness of breath and of temper. If I seem frustrated, it's not with you, it's with my damned lungs. Too, I thank you in advance and retroactively for your patience and understanding, and for your help in ensuring that I only talk when needed, and then only as much as I need to to make my point.

So...what have we got to do to nail things down?

In calculus we'll be finishing up with a little bit more on curve sketching, a treatment of L'Hôpital's Rule, maybe a little Newton's Method. Y'know. Fun stuff. I'll be fitting in one more miniproject, a couple more quizzes, and one more exam, on Chapter 4, before the final wraps things up.

Only a few more days remain in Number Theory and 280; in each, I've got two more days to say my piece before I turn things over to the students. I'm excited about the presentations folks are putting together. In 368 we'll devote whole class periods to the Riemann zeta function and the Riemann hypothesis, to groups of arithmetic functions, to extended properties of Gaussian arithmetic, and to algebraic cryptography. In 280, folks are putting together 15-minute presentations on Ramsey theory, the Fibonacci sequence, Euler's identity, the cardinality of sets of subsets of the naturals, on Pythagorean triples, and so forth. I'm looking forward to it.

Meanwhile, on Sunday I've gotta drive a few hours to the north to James Madison U. to give another talk on detecting hyperbolicity using asymptotic connectivity, assuming I'm well enough.

Oh, the pizza man just drove up outside, I'd best be off for now.

Remind me to post again later on the idea that struck me while lying awake in a codeine-induced stupor last night: The Multimedia Menger Sponge Project. And about another (a 9th! horrors!) student pet peeve I thought of this afternoon. Not to be missed!

Friday, April 06, 2007

But I get the feeling that more people would be gung-ho about mathematics if they'd not been actively turned off to it somewhere along the road from K to 12.

Last week those cute little kiddies in my Super Saturday program got visibly excited about the L-tiles I had them playing with. They really went to town on those suckers.

I mocked these babies up out of particolored poster board to work on induction with the 280 folks earlier this semester, and I realized then that they'd make a great toy for introducing fractals to the Super Saturday kids. Thus I spent several hours here and there during the past few weeks cutting out a few hundred more tiles, giving myself enough stock to build truly titanic Ls.

And so we did, last Saturday. Five of the seven in the class eagerly worked away, fully cooperating with one another, offering friendly suggestions and pointers, gradually piecing together the L10 monster with 100 tiles in it. (Meanwhile I had to keep the other two from braining each other with a half-empty bottle of Aquafina.) It didn't take long for the sharpest among them to detect the patterns one needed to build larger and larger Ls; if I'd let them, I'll be they would have started work on the L20, though I doubt I had enough Ls to make that one work.

So here's my question: how is it that five bright elementary schoolers were more excited about mathematical discovery than a roomful of math majors? Granted, the stakes are lower in Super Saturday: no assignments, no grades, no deadlines, not to mention the fact that the young 'uns are simply living one of the most carefree periods of their lives. But all that aside, aren't math majors supposed to...oh, how shall I put this?...like math? When faced with designing larger and larger Ls in our 280 class, the reaction from many was disinterested torpor. A few were definitely engaged, but most looked on languidly.

What do we do to these poor kids before they get to college?

We teach them to take tests.

We teach them that math is hard, and only really smart people can do it.

We teach them that "proof" and "poorly-taught high school geometry" are synonymous.

By the time they get to my calc class, I've got to do all I can to convince them that if math isn't fun, then at least maybe it's useful.

Today I found myself explaining to my Calc I kiddies why it is we care about minima and maxima, and like a good little moneymaker, I pulled out the example of a profit curve. A good example, and a sure justification for differential calculus...but why not care about Fermat's Theorem for its own sake? It's a really beautiful theorem, and the road to its discovery is a storied one involving the arduous work of many of history's brightest minds.

I could have said this, yes, but the cold I'm trying to kick has taken the edge off, and I didn't have the energy to fight today what might in most classrooms be an uphill battle. (Would it be so in my classroom?)

Tomorrow morning my Super Saturday kiddies and I are going to work at building a model of the Menger sponge, a "3-d" fractal that we'll put together out of 400 tiny cubes of paper that we'll fold ourselves. You should have seen how stoked these kids were last week when we made that our plan.

Next week, what? Codes 'n' cryptography? More fractals? Who knows.

Next week in 280? Relations. Beautifully flexible, eminently useful: order relations alone make the careers for hundreds of brilliant mathematicians (and in no small measure have contributed to my own).

Wednesday, April 04, 2007

It's especially frustrating in classes like Calc I, where I've "got to" get to a certain point in the curriculum so that my kiddies won't be left in the dark when a new semester's sun rises on Calc II.

My colleague on the third floor, Fyodor, mentioned in passing this morning that he's happy if his Precalc students end the semester with a basic and lasting understanding of polynomials and rational functions. I concurred.

And I meant every word I said to my Calc class this afternoon in the aftermath of yesterday's exam: "I don't put too much stock in grades." A partial truth. "I'm much more concerned with progress." Closer still to the mark. "If you leave this room with a greater commitment to critical thinking, if you gain facility in performing a few mathematical calculations, if you can grasp the basic concepts behind calculus and how they relate to the 'Big Picture,' then you've succeeded."

Monday, April 02, 2007

Let's say that the instructor waltzes in and announces that you're going to be working in groups. You can't call on your best friend in the class to help you; the instructor's choosing the groups for you, and the way you're all split up appears to be random. Oh great, you're stuck with Jessica. You heard about her. Giselle you don't know, except for the fact that her cell phone's gone off in class three times so far this semester. And then there's Dante. You've never heard him say a word. You're given five minutes at the end of class to meet with your new group members, to get to know each other a little, to exchange contact information. You've got a week and a half to put together the project just assigned, and you want to get to work on it as soon as possible.

As early as your first meeting, two days later, you notice certain interpersonal dynamics. You're focused and on-task (or at least you try to be), while Giselle is not. She gets up every five minutes to get a snack from the vending machine or call her best friend on her cell. Meanwhile Dante has started to work on the project, but he's off in his own world, performing computations that you don't understand and that he seems unwilling to explain to you. That leaves you and Jessica, and you find her to be (quite frankly) dumb as a box o' rocks. Indeed, almost every other sentence out of her mouth is "I don't know."

"Well, did you understand this one?"

"I don't know."

"What did Prof. Buxfizz say about this method?"

"I don't know."

"What in the hell is taking Giselle so long this time?"

"I don't know."

What good could come of working with her? You finally decide to peer over Dante's shoulder as he works away at the project's first problem. At least maybe you can learn a little by looking on.

Do any of these habits sound familiar? Chances are quite good that you've observed one or more of these personalities in group work you've done in class. Maybe you're Dante, maybe you're Giselle. Maybe you're the poor overtasked Jessica, or maybe you really are the monkey in the middle whose role I've given to you as our fictional observer.

Last week my Learning Circle colleague Darlene pointed out that when small groups convene, very predictable personalities manifest themselves. There are type-A leaders who take it upon themselves to see that everything's done right, often dominating the workload and shopping the simpler tasks out to the others. There are the absent slackers, who more often than not don't bother to show up. There are the silent types who are afraid to speak up, fearing they'll betray their ignorance and be laughed at. There are the dittoheads who go along with every answer uncritically, there are the speed-demons who just want to finish everything as quickly as possible, and there are the perfectionists who aren't happy until the seventeenth draft of the group's write-up has at last been produced in the optimal font-size.

What type are you? I've only recently (in the past couple of years) begun to appreciate that successful performance in group work really does require of one an awareness of the sort of persona one tends to take on in group get-togethers. (Likewise, it's not enough for me as a teacher to simply throw the groups together and say, "have at it!") To get a group up and running, you've got to do more than make sure there's a time available for everyone to meet: once all are assembled in one place, there's then the matter of getting everyone to contribute her or his fair measure, to the extent that each is able to contribute according to her or his talents.

What is your talent? What good do you typically contribute to a group endeavor? Can you ask yourself to contribute your share of your positive energy, and can you challenge yourself to minimize your adverse behaviors? Can you bring yourself to contribute something else that's usually left inside of you?

I mentioned in my last post that throughout my schooling I was always the "get it done" guy. I'd rather do all the work myself than let the slower folks in the group take control and botch it up. Of course, having now spent a long time on the "other side of the glass," I realize that this attitude probably rendered all group exercises practically useless for my teammates, but hey: I got what I needed out of it, and everyone got to share in the good grades. Win-win, right?

Now in group work I challenge myself to stay quiet, to not dominate. I contribute, but I wait for contribution from others. I make sure my piece is heard, but I do what I can to incorporate others' views with my own, and whenever I can I paraphrase, reiterate, recount, others' takes on things to make sure that I'm understanding them properly. I offer help when it's needed and do what I can to facilitate the others' learning. If I find myself in danger of dominating the conversation, I try to shut up.

What if you were Jessica? Could you challenge yourself to speak up? This must be hard! Though it's somewhat awkward for me to sit on my hands on not go as quickly as I know I could if working alone, I realize that it must be downright terrifying for a shy and unsure group member to risk the derision of her peers by admitting that she doesn't know what in the hell is going on. Last semester in MATH 365 there was one group in which three of the group's members were decidedly more self-assured than the fourth. This fourth frequently confided to me about how difficult it was to tell his friends to "slow down! I can't understand things as quickly as you all can."

And Giselle, what could she do? Perhaps her challenge at the outset would be simply to stay in the moment and keep her focus. And you, the nameless observer in the comedy above? Could you, perhaps, challenge yourself to be the one to bring the group together? Could you make it your place to call "time out" and reconvene the group to say, "all right, folks, we're just not on the same page on this one. Can we lay out a plan that'll work for everyone?"

I don't know. I don't think there's any one right answer. Every situation is different.

Sunday, April 01, 2007

How 'bout that? It's taken me a while to make that first hundred, as rarely as I've been posting this semester. It's happened that most of the time when I've thought, "huh, that's an interesting thought. I might could write about that," I've ended up being too busy to post it before forgetting about it again. (Me? Busy?)

I've come to realize that for the most part, bloggers are either

1. college freshpeople who have more time on their hands than they know what to do with, writing about why Green Day is the greatest band in history (hint: they're not), or

2. pseudo-intelligent ex-English majors working in the food-service industry, writing about the brilliant conversation on Sartre they shared with the checkout guy at the Piggly Wiggly, and who think that now that they're blogging everyone's gonna find out what sort of genius they possess and that they're sure as hell gonna land that six-figure book advance.

Considering these options, it's probably best that I don't often have time to blog.

Nevertheless, I do corner a few seconds here and there, and sometimes those few seconds come at a time when I happen to be thinking about my teaching, specifically or generally.

Like now.

I just spent an hour or so hanging out in the comments section of one of my favorite blogs (Waiter Rant). Recently he (the anonymous New York-based blogger going by the name "Waiter") devoted a couple of posts to "assholes": one post listed 50 signs that you might be an "asshole customer"; a second, 50 signs that "your server might be an asshole."

This makes me think of an exercise I recently read in Maryellen Weimer's Learner-centered teaching, a work I referenced a few posts back, and which has given me a number of neat ideas to try out in my own classes.

Saith Prof. Weimer: think about starting the semester off with a brainstorming activity in which your students finish open-ended sentences like "I find that I learn well in a classroom where..." or "I find it annoying when the professor...". Let them discuss the matter, arrive at a consensus. This exercise promotes reflection on the learning process and on creating environments conducive to learning, and can serve as a prelude to a "classroom contract" in which the instructor agrees to work to construct an environment where the students' admitted concerns are addressed, and in response, the instructor can offer up a short list of behaviors s/he finds annoying in students and ask that the students do their best to avoid said behaviors.

Both I and my sole colleague in this semester's Learning Circle (shout out, Darlene!) agreed that this activity would probably seem condescending in an upper division class, but it might be a useful one to pull on first-years at the semester's outset.

Why not try it now? I'll share with you a list of my own pedagogical pet peeves, and in response, I hope you can feel free to share yours with me. I'm not claiming that any of my current students are guilty of any particular charge, but you might just recognize yourself in one or two of them. If you do, I hope that you'll do what you can to rein it in. As you'll know if you've been in one of my classes, I'm an easy-going guy, and I'm not likely to tear you a new one if you occasionally step out of line, let your cell phone ring because you sincerely forgot to set it to vibrate, can't seem to stay awake because you were up all night cramming for your Organic midterm, come in unprepared every now and then...I'll let it go, because I know we all have days like that, and I'm not an ogre.

And I like my students. I really like you guys. I have to say that in the almost-decade I've been teaching at the college level, of the roughly 700-800 students I've had in my charge at one time or another, I've personally liked about 99.5% of them. There have been a small few who've rubbed me the wrong way, a couple here and there that've gotten my cheese for one reason or another, but at the end of the day, I can literally count on one hand the number of students I've had whom I just couldn't stand. Really. You wanna know how many? Two. For real. Just two, and neither at UNCA. One at Vanderbilt University (initials RG), and one at the University of Illinois (initials KC). That first was a real piece of work. Remind me to tell you about his golf game up in Kentucky sometime.

If you find yourself identifying with one of the annoyers in the list below, please remember that it's the annoying habit I despise, not the person performing it. Chances are really good that I like you, and I want to continue to work with you as best I can. Just cut the crap, and we'll get along fine.

With no further ado, let me present you with

8 Annoying Student Habits(I honestly couldn't think of any more. See how easy-going I am?)

1. I'm annoyed by endless complaints about how long it takes one to do one's homework (in my class or someone else's). Complaining about it doesn't finish it, it doesn't make it any easier, and it's not going to earn points from your professor (me included). If I think an extension is warranted (and often one is), I'll figure that out for myself, I don't need your help. Note: freshpeople are most often guilty of this behavior, as they've generally got a pretty poor sense of how much homework is "appropriate." By the way, I'll almost guarantee you that I spend at least twice as much time (often much more) in thinking up, designing, writing, photocopying, posting, grading, commenting on, and returning any single assignment or exam than you do in completing it. (If you ever wanna know how long a particular assignment took me to process, I'd be glad to give you an estimate, it's probably longer than you think.) Please keep that in mind before lodging a complaint.

2. It annoys me when students ask in class about course information that's available on the website. This isn't a big issue, but it's an annoying one nonetheless. I keep a pretty well-stocked website (this too takes a lot of time to maintain properly); if something's not listed/available from the course website, chances are it's not all that important. So if you've missed a couple of days of class and you need to find out what homework was assigned while you were gone, please don't ask me to spend three minutes at the beginning of class tracking that information down for you.

3. In the same vein, if you miss a few class periods, please don't expect me to give you a "synopsis" of the classes you missed. If you had a valid excuse for being gone, I might very well be able to spare 10-15 minutes to brief you on what went down while you were away, but I'm much more likely to actually give you this time if you've taken time beforehand to prepare for this briefing by reading the material we covered in your absence ahead of time.

4. Please don't complain about having to work in a group. I don't care if you don't like to work in groups. You know what? Not all of us do. I include myself in that list. I've always been one of those folks who wants to do everything for himself because he's not quite sure anyone else is going to do it as well as he will. You know what else? At some point in life, you're going to have to work in groups. It's called "committee work," another term for "hell." The experience in group work you gain now, in the relatively low-stakes, comfortable, safe environment of your classroom, the better you'll be at it in the future.

5. I've never been a huge fan of going over homework problems in class if doing so is not an integral part of the course's design (as is the case in my current 280 and 368 courses), especially if the students are not the ones doing the "going over" (see previous parenthetical comment). Some profs like to devote a good chunk of time to going over homework problems, while I, most of the time, don't. Occasionally I'll find it worth the class's while to go over the odd problem, but I'd rather you not ask me at the beginning of every class, "can we go over Problem 346?"

6. In classes where the solutions manual is broadly available, it annoys me to no end when students submit homework which was clearly copied from the manual. The manual can be a useful tool, if used properly, but it's worse than useless if the only purpose it serves for one is as a crib sheet. In the end, it's usually the student's loss, for a few extra points on the homework will be more than counterbalanced by the smack in the face the hapless student'll get come exam time when the solutions manual is unavailable for consultation.

7. Obvious obliviousness on the students' parts annoys me. If you're not gonna mind what I'm sayin' at all, then go home. If you're going to be your group's fifth wheel, go home. If you just can't be bothered to stay awake, go home. If you'd rather sit back and check out the box scores (Spring 2006, Calc II, Section 1?) in the sports section than focus on what the rest of the class is doing, go home.

8. Hateful speech. I hope this goes without saying, but for Pete's sake, people: please don't be crackin' "jokes" or whippin' off "smart" remarks about others' color, gender, ethnicity, nationality, religion, sexual preference, disabilities, intelligence, and so forth, whether it's in general or specific terms. There's really no room for that kind of thing anywhere in this world, and there's sure as heck no room for it in my class.

***

That's it, for now. Honestly. That's all I can think of off the top of my head. I'm probably in the minority, but little things like inadvertent cell phone rings and discreet lunch-eating don't get to me much. I don't even mind class clowning, if it's not too rambunctious or mean-spirited. It's just the big things, really.

So how 'bout it, Studenten? What professorly habits annoy you? What things have your profs done in the past (no names needed!) that you really could have done without? I'm truly curious.

In case the news hasn't trickled your way yet, my grant was picked up: this past Monday I learned that UNCA has been awarded an NSF grant to run a Summer Research Experience for Undergraduates program in mathematics.

I'm excited. And terrified.

What this means, of course, is that I will have to forgo sleep for a while. Maybe until August.

In the next month we'll be selecting eight talented undergrads from around the country to take part in an eight-week research program in the fields of group theory, graph theory, and geometry, all writ large. We'll hit everything from network stability to celestial mechanics.

I found out about it last Monday afternoon around 4:30 p.m. I ran home, jubilant. It was Tuesday night that the notion really started to sink in; I think I must have gotten an hour or so of sleep. Between worry over whether or not I'll be able to get everything lined up for the start of the program and these damned seasonal allergies (or is it really a cold?) I couldn't get a wink.

Ah, well.

That's all for now on that matter. I feel like I've got loads to say, but no words to say it with.